Research ArticlesNo Access

Bowling ball representations of braid groups

Department of Mathematics, University of California, Santa Barbara, CA93106, USA

https://doi.org/10.1142/S0218216518500359Cited by:0 (Source: Crossref)

Abstract

In a remark in his seminal 1987 paper, Jones describes a way to define the Burau matrix of a positive braid using a metaphor of bowling a ball down a bowling alley with braided lanes. We extend this definition to allow multiple bowling balls to be bowled simultaneously. We obtain representations of the Iwahori–Hecke algebra and a cabled version of the Temperley–Lieb representation.

Keywords:

AMSC: 20F36, 57M27

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